# nLab homotopy 2-category

### Context

#### Higher category theory

higher category theory

# Contents

## Idea

The homotopy 2-category of an (∞,n)-category $\mathcal{C}$ is the 2-category $Ho_2(\mathcal{C})$ with the same objects and 1-morphisms as $\mathcal{C}$ and with the 2-morphisms being the equivalence classes of 2-morphisms of $\mathcal{C}$.

In other words, for every pair $X,Y$ of objects in $\mathcal{C}$, the hom-category $Ho_2(\mathcal{C})(X,Y)$ is the ordinary homotopy category of the $(\infty,n-1)$-category $\mathcal{C}(X,Y)$.

Created on August 23, 2012 at 16:32:42. See the history of this page for a list of all contributions to it.